My Improv 4 came stock with 2 EMG CS pups & an EMG BTS preamp. If the EMG 35P4 doesn't really capture the classic "P" sound do you know if there is any Active pup (That comes in a humbucker housing) that will come close?

Only thing I can think of is a Bartolini M3 series (EMG35 shape) pickups. They might give you more of what you're looking for. Thing is, a really classic P tone is gonna come from passive pickups more easily than Active versions.